Answer to Question #173859 in Statistics and Probability for Rustom

Question

You already know how to convert a random normal variable to a standard normal score or z-score. This time, let’s do the reverse. Given the z-score, compute for the raw scores. Problem number is done as an example to guide you. Problems 2 and 3 are given to you.

2. Given: 𝑥 = 75, 𝑠 = 10. What is the raw score when 𝑧 = −1.56?

1. Use the computing formula for finding the z-score for sample data. You can derive the formula for easy computation.

2. Write the given values

4. Substitute the given values in the computing formula. Then, compute the raw score (𝑥).

3. Given: 𝜇 = 48,𝜎 = 5.5. What is the raw score when 𝑧 = 2.43?

1. Use the computing formula for finding the z-score for sample data. You can derive the formula for easy computation.

2. Write the given values.

3. Substitute the given values in the computing formula. Then, compute the raw score (𝑥).

Answer 1

2.

1.

$$z=\dfrac{x-\bar{x}}{s}$$

$$x=\bar{x}+zs$$

2.

$$\bar{x}=75, s=10, z=-1.56$$

4.

$$x=75+(-1.56)(10)$$

$$x=59.4$$

3.

1.

$$z=\dfrac{x-\mu}{\sigma}$$

$$x=\mu+z\sigma$$

2.

$$\mu=48, \sigma=5.5, z=2.43$$

3.

$$x=48+(2.43)(5.5)$$

$$x=61.365$$